Exploration of Epistemological Limits: The Necessity from Logical Zero Point to Physical Infinity

We propose a complete derivation from logical self-sufficiency to physical reality. The starting point is not metaphysical questions about "existence versus nothingness," but the self-referential necessity of logic. We prove that: (1) Binary discrimination (0/1) is the minimal logical structure; (2) The digital tower (recursive sequence generation) necessarily contains all possible information (cardinality $2^{\aleph_0}$); (3) Mathematics itself emerges from the adjacency relationship between digits, not as a prior foundation; (4) Algorithms are self-consistent structures of state traversal; (5) State space is an abstraction of the digital tower; (6) Topology and symplectic geometry necessarily emerge from variational principles; (7) Time, quantum mechanics, and particles are derived from the geometric properties of state space; (8) Observers geometrically necessarily emerge at critical complexity (seed model verification: phase transition $p_c \sim 1/\ln N$). Core proposition: Mathematics is not a prior foundation of physics, but a modeling language emerging from more fundamental logical-computational structures. Physical reality is a self-consistent computational process. The emergence of observers is not accidental, but a geometric necessity when complexity reaches a threshold. Keywords: Logical self-sufficiency, Digital Tower, Mathematical Emergence, Algorithmic Ontology, State Space, Symplectic Geometry, Observer, Universe Selects Observers (USO) Full text length: ~20,000 wordsRigor level: Medium-High (speculative parts clearly marked)